Question

Find the perimeter of the square.

Short answer

The required perimeter of the square is 288

Step-by-step solution

Step-1 – Given

Given two sides of the square are $9x$ and $5x+32$.

Step-2 – To determine

We have to find the perimeter of the square.

Step-3 – Calculation

We know that each sides of a square are equal.

So, $9x=5x+32$

Then we solve the equation:

$\begin{array}{l}9x=5x+32\text{writetheequation}\\ 9x-5x=32+5x-5x\text{subtract5xfrombothsides}\\ 4x=32\text{simplify}\\ \frac{4x}{4}=\frac{32}{4}\text{divideeachsideby4}\\ x=8\text{simplify}\end{array}$

Substituting the value of x in the expression of a side = $9x$ we get:

$\begin{array}{l}9x\\ =9\times 8\text{Substitutethevalueof}x\\ \text{=72Multiply}\end{array}$

So the length of each side = 72

Hence,

$\begin{array}{l}\text{Perimeter}\left(P\right)=4\times \text{eachsideofthesqaure}\\ \text{Perimeter}\left(P\right)=\text{4}\times 72\text{Substitutethevalueintheformula}\\ \text{Perimeter}\left(P\right)=288\text{unitsMultiply}\end{array}$

Therefore, $\text{Perimeter}\left(P\right)=288$